Recombination and selection are two major evolutionary mechanisms that influence the pattern of variation in genomes. Efforts to deduce patterns of historical recombination are central to the design and analysis of disease association studies, and the ability to identify targets of selection may have important implications for biomedical research. The long-term objective of this application is to characterize quantitatively the effects of recombination and selection on genomic variation. Efficient algorithms and rigorous mathematical techniques will be developed for accurate inference in population genomics. The specific aims of this application are: Aim 1: Develop methods to assess Monte Carlo approaches to likelihood computations in the coalescent with recombination. Deterministic, algorithm-based methods will be developed to compute likelihoods very accurately, opening up a new window of opportunities for testing and fine-tuning Monte Carlo approaches to likelihood computation. For input data of moderate size, the newly developed tool will be used to evaluate existing Monte Carlo methods. Aim 2: Develop methods to characterize historical crossover and gene-conversion recombinations. A general mathematical framework based on diffusion approximation will be developed to obtain accurate multi-locus conditional sampling distributions. Using that approach, a method that can jointly estimate crossover and gene-conversion rates will be developed. Further, existing estimation methods will be revisited and specific computational improvements will be made. : Aim 3: Study the interaction of natural selection at multiple loci. The interaction of selection at multiple loci will be studied analytically and the structure of LD shaped by interacting selection will be characterized. Fixation probabilities under multi-locus selection will also be studied. [unreadable] Relevance: Understanding the pattern of variation in the human genome is central to the study of the genetic basis of disease risk and variability in drug response. The aim of this research is to develop accurate methods to characterize various evolutionary mechanisms that shape the pattern of genomic variation.